Saturation-aware robust optimal operation control of microgrids based on minimum-regret optimization

Technical Summary: Saturation-aware Robust Optimal Operation Control of Microgrids Based on Minimum-Regret Optimization

Problem Statement
The paper addresses the robust optimal operation control of islanded microgrids (MGs) characterized by a high penetration of renewable energy sources (RES) and uncertain load demand. Conventional energy management systems (EMS) often fail to account for the specific dynamics of lower control layers, such as droop control and the physical saturation limits of units (power and energy bounds). This omission can lead to a mismatch between predicted and actual system behavior under disturbances. While existing robust approaches, such as min-max Model Predictive Control (MPC), ensure feasibility under worst-case scenarios, they often result in conservative operation that ignores the potential for near-optimal performance in non-worst-case scenarios. The core challenge is to design a control strategy that remains feasible across a wide range of uncertainty realizations while minimizing the "regret"—the performance gap between the chosen control action and the optimal action for a specific scenario realization.

Methodology
The authors propose a hierarchical control structure that integrates a saturation-aware primary control layer with a robust MPC-based EMS.

1. Saturation-Aware Primary Control: The lower layer employs droop control with autonomous power and energy limiting. The model explicitly incorporates saturation functions at the physical limits of conventional units, storage units, and RES. This ensures that power sharing is maintained even when units hit their operational bounds.
2. Minimum-Regret Formulation: The upper layer formulates a robust MPC problem (Problem 1) that seeks to minimize the maximum regret across all possible disturbance scenarios (renewable generation and load demand). The objective is to find a control trajectory that performs as close as possible to the scenario-specific optimal cost for every realization of uncertainty.
3. Tractable Solution Approach: Recognizing that the direct solution to the minimum-regret problem is computationally challenging due to binary variables and inner optimizations, the authors develop a simplified, tractable approach (Problem 2):
   • Constant Setpoints: Under the assumption that conventional units are always on, the authors derive constant power setpoints ($u^*$) based on Proposition 1. These setpoints are designed to create non-overlapping linear droop regions, enforcing a specific priority: RES are utilized first, followed by storage (charging/discharging based on state of charge), and finally conventional generators.
   • Robust Unit Commitment: The EMS solves a robust unit commitment problem where the continuous power setpoints are fixed to the values derived in Proposition 1. The optimization variable is restricted to the switching states ($\delta_t$) of the conventional units. This allows the system to robustly satisfy constraints and minimize the worst-case cost by deciding which generators to enable or disable, while relying on the saturation-aware droop control to handle real-time power balancing.

Key Contributions

• Minimum-Regret Framework: The paper formally states a minimum-regret robust MPC problem for microgrids, moving beyond the conservative nature of traditional min-max MPC to optimize performance across all disturbance scenarios.
• Saturation-Aware Modeling: The work integrates physical saturation limits and droop control directly into the EMS design, addressing the mismatch often found in literature where lower-layer dynamics are ignored.
• Rule-Based Constant Setpoints: The authors prove that specific constant power setpoints can achieve optimal operation under an "always-on" assumption for conventional units. This theoretical result simplifies the complex robust optimization into a manageable unit commitment problem.
• Hierarchical Control Design: The proposed strategy combines autonomous primary control (handling saturation and power sharing) with a robust secondary EMS (handling unit commitment and uncertainty), offering a computationally efficient alternative to full-scale robust MPC.

Results
The proposed controller (Problem 2) was evaluated in a case study involving an islanded microgrid with a conventional generator, storage, PV, wind, and load. The performance was compared against a "prescient" controller (which knows future uncertainties perfectly) and a saturation-aware min-max MPC from prior work [12].

• Cost Performance: The proposed robust unit-commitment EMS achieved a total closed-loop cost very close to the prescient controller across all tested scenarios (ranging from worst-case to best-case).
• Comparison with Min-Max: The proposed method consistently outperformed the saturation-aware min-max MPC [12] in non-worst-case scenarios. The min-max approach incurred higher costs because it optimized solely for the worst-case, whereas the proposed minimum-regret approach leveraged available renewable power in less adverse conditions.
• Trade-offs: A slight performance gap remained between the proposed method and the prescient controller. The authors attribute this to the restriction of using fixed priority-based setpoints, which may not capture the optimal behavior when switching costs and fixed generation costs incentivize operating conventional units more intensively for shorter durations to store energy.

Significance and Claims
The paper claims that the proposed strategy offers a viable and computationally efficient solution for the robust operation of microgrids with high RES penetration. By utilizing constant, saturation-aware setpoints and focusing the optimization on unit commitment, the approach simplifies the control problem while maintaining near-optimal performance. The authors suggest that this method is particularly well-suited for small-scale microgrids due to its simplicity. The work demonstrates that it is possible to achieve near-optimal operation under uncertainty without the computational burden of solving a full multi-scenario robust MPC with binary variables and continuous setpoints simultaneously. Future work is identified as focusing on larger microgrids and broader uncertainty sets.